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Factors affecting soil permittivity and proposals toobtain gravimetric water content from time domainreflectometry measurementsThring, L.m.; Boddice, D.; Metje, N.; Curioni, G.; Chapman, David; Pring, L.

DOI:10.1139/cgj-2013-0313

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Citation for published version (Harvard):Thring, LM, Boddice, D, Metje, N, Curioni, G, Chapman, D & Pring, L 2014, 'Factors affecting soil permittivityand proposals to obtain gravimetric water content from time domain reflectometry measurements', CanadianGeotechnical Journal, vol. 51, no. 11, pp. 1303-1317. https://doi.org/10.1139/cgj-2013-0313

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ARTICLE

Factors affecting soil permittivity and proposals to obtaingravimetric water content from time domain reflectometrymeasurementsL.M. Thring, D. Boddice, N. Metje, G. Curioni, D.N. Chapman, and L. Pring

Abstract: Time domain reflectometry (TDR) measures the apparent relative dielectric permittivity (ARDP) of a soil and iscommonly used to determine the volumetric water content (VWC) of the soil. ARDP is affected by several factors in addition towater content, such as the soil’s electrical conductivity, temperature, and density. These relationships vary with soil type and arevery soil-dependent, and despite previous research, they are still not fully understood. A multivariate statistical approach(principal component analysis, PCA) is used to describe a range of soils from two separate sites in the UK (clay and silty sand –sandy silt). The advantage of a PCA is that it considers several variables at a time, giving an immediate picture of their underlyingrelationships. It was found that for the studied soils, ARDP was positively correlated with VWC and bulk electrical conductivity,but did not show any dependence on some other geotechnical parameters. TDR has recently been used in geotechnical engi-neering for measuring the gravimetric water content (GWC) and dry density. However, the current approaches require acustom-made TDR probe and an extensive site specific empirical laboratory calibration. To extend the potential use of TDR in thegeotechnical industry, three relatively simple methods are proposed to estimate the GWC from VWC (derived from the measuredARDP values) and dry density depending on the amount of information known about the soil. Examples of possible applicationsof these methods include continuous monitoring of consolidation adjacent to a structure, the effect of seasonal weather andclimate change on ageing earthwork assets, and the shrink–swell potential adjacent to trees. All three methods performed well,with between 83% and 98% of the data lying within a ±5% GWC envelope, with the data for clay soils performing better than thosefor silty sands – sandy silts. This is partly due to the fact that the applied relationship converting ARDP to VWC performs betterfor clays than silty sands – sandy silts, as well as less variation of the estimated bulk density that is needed to derive the drydensity.

Key words: time domain reflectometry, volumetric water content, gravimetric water content, apparent relative dielectric permit-tivity, principal component analysis, estimation of dry density.

Résumé : La réflectométrie dans le domaine temps (RDT) mesure la permittivité diélectrique apparente relative (PDAR) d’un sol,et est communément utilisée pour déterminer la teneur en eau volumique (TEV) de ce sol. La PDAR est affectée par plusieursfacteurs en plus de la teneur en eau, comme la conductivité électrique du sol, la température et la densité. Ces relations varientselon le type de sol, et malgré les recherches antérieures, elles ne sont pas encore bien comprises puisqu’elles dépendentbeaucoup du sol. Une approche statistique multivariée (analyse en composantes principales, ACP) est utilisée pour décrire unevariété de sols provenant de deux sites différents au Royaume-Uni (argile et sable silteux – silt sablonneux). L’avantage de l’ACPest qu’elle considère plusieurs variables a la fois, ce qui permet d’obtenir une image immédiate de leurs relations. Il a étédéterminé que pour les sols étudiés, la PDAR est corrélée positivement avec la TEV et la conductivité électrique totale, mais nedémontre pas de dépendance sur les autres paramètres géotechniques. La TEV a été récemment utilisée en géotechnique pourmesurer la teneur en eau gravimétrique (TEG) et la densité sèche. Cependant, les approches actuelles nécessitent une sonde RDTfabriquée sur mesure et un calibrage empirique en laboratoire spécifique et détaillé. Afin d’étendre l’utilisation de la RDT dansl’industrie géotechnique, trois méthodes relativement simples sont proposées pour estimer la TEG a partir de la TEV (dérivée devaleurs de PDAR mesurées) et la densité sèche dépendamment de la quantité d’information connue a propos du sol. Desexemples d’applications possibles de ces méthodes comprennent le suivi en continu de la consolidation adjacente a unestructure, l’effet du climat saisonnier et des changements climatiques sur le vieillissement d’ouvrages en terre, et le potentiel deretrait–gonflement a proximité des arbres. Les trois méthodes performent bien, avec 83 % a 98 % des données situées a l’intérieurde l’enveloppe ±5 % TEG, avec les données pour les sols argileux offrant des meilleures performances que celles des sablessilteux – silts sabonneux. Ceci est dû en partie au fait que la relation appliquée pour convertir la PDAR en TEV donne de meilleursrésultats pour les argiles que pour les sables silteux – silts sablonneux et une variation plus faible de la densité totale estimée, quiest nécessaire pour dériver la densité sèche. [Traduit par le Rédaction]

Mots-clés : réflectométrie dans le domaine temps, teneur en eau volumique, teneur en eau gravimétrique, permittivité diélec-trique apparente relative, analyse en composantes principales, estimation de la densité sèche.

Received 15 August 2013. Accepted 23 May 2014.

L.M. Thring. Arup, The Arup Campus, Blythe Gate, Blythe Valley Park, Solihull, B90 8AE, UK.D. Boddice, N. Metje, G. Curioni, D.N. Chapman, and L. Pring. School of Civil Engineering, College of Engineering and Physical Sciences, Universityof Birmingham, Edgbaston, Birmingham, B15 2TT, UK.Corresponding author: N. Metje (e-mail: n.metje@bham.ac.uk).

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Can. Geotech. J. 51: 1303–1317 (2014) dx.doi.org/10.1139/cgj-2013-0313 Published at www.nrcresearchpress.com/cgj on 29 May 2014.

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IntroductionTime domain reflectometry (TDR) is an electromagnetic (EM)

technique commonly used to measure the soil volumetric watercontent (VWC). Since the development of a general calibrationrelationship between the TDR measured apparent relative dielec-tric permittivity (ARDP) and VWC by Topp et al. (1980), severalother calibration equations have been presented by variousauthors (e.g., Ledieu et al. 1986; Roth et al. 1990; Wensink 1993;Curtis 2001). There is huge variation in the perceived significanceof different soil properties on the measured ARDP (van Dam et al.2005). ARDP has been shown to depend on the soil density (Ledieuet al. 1986; Malicki et al. 1996), temperature, (Or and Wraith 1999;Skierucha 2009) and bulk electrical conductivity (BEC) (Bittelliet al. 2008). Other authors have also found relationships betweenARDP and geotechnical parameters such as liquid limit (LL) andlinear shrinkage (LS) (Thomas et al. 2010a). Despite the consider-able number of previous studies, the relationships between ARDPand soil parameters vary with soil type, and are still not fullyunderstood.

A disadvantage of the TDR technique is that it often requiressoil-specific calibration between ARDP and water content, requir-ing laboratory tests (Jacobsen and Schjonning 1993; Quinoneset al. 2003). This calibration is required for every probe arrange-ment as the cable length and attachments have been shown toaffect the measurement of ARDP (Logsdon 2000). In recent yearsTDR has been deployed in geotechnical engineering for measur-ing the gravimetric water content (GWC) and dry density (Yu andDrnevich 2004; Drnevich et al. 2005; Jung et al. 2013). However,these methods use a specifically designed probe type and alsorequire laboratory calibration. This tends to limit the use of TDRin the geotechnical industry.

The aim of this paper is two-fold: (i) to investigate the factorsaffecting the measurement of ARDP by means of a multivariatestatistical approach on a number of soils from the UK, and (ii) todevelop rapid methodologies for measuring GWC in the field withcommercial TDR without the need for laboratory tests. Further-more, the paper uses the TDR data obtained in this research inexisting empirical and semi-empirical relationships to determinethe applicability of these methods to the current data set.

To fulfil these aims, laboratory testing was carried out on arange of soil types, at different water contents and temperatures,and a consistent methodology was developed to prepare uniformsoil samples. Tests were performed by relatively inexpensive com-mercial TDR equipment using the standard travel-time analysis.The data were analyzed by means of the principal componentanalysis (PCA) technique, which is not commonly used in geotech-nical engineering but has been demonstrated to be a useful ap-proach to study a multivariate system such as the soil (Jolliffe2002).

The novelty of the presented work is not in the laboratory meth-odology or the use of TDR probes, but the use of the data gener-ated for two distinctly different soils at VWC between 0% and 50%,as well as three different temperatures, that also adds to theknowledge base in this field. The novelty of the presented worklies in the application of the PCA to these types of data as well asthe attempt to correlate TDR measurements to GWC, as is usedmore commonly by the geotechnical engineering industry. Themethods proposed use either existing laboratory data for drydensity, or estimate the dry density using two different methodsbased on simple descriptions of the soil.

Theoretical background

Principles of permittivityRelative dielectric permittivity is the ratio between the absolute

permittivity of a material and the absolute permittivity of freespace (�0, 8.85 × 10−12 F/m), and expresses the ability of a materialto polarize under an electric field (Ledieu et al. 1986). In this paper

the relative dielectric permittivity will simply be referred to aspermittivity. To measure the ability of a material to polarize, itcan be placed into an alternating EM field, and the time it takes forthe wave to travel through the material is measured. This time isknown as the transit time. In TDR, a probe is inserted into the soiland the transit time of an EM wave along the probe can be mea-sured, and therefore the propagation velocity of the wave found(Ledieu et al. 1986). Propagation velocity can be used to derive adimensionless value of the permittivity of a soil that is often re-ferred to as ARDP in the literature (Topp et al. 1980).

Permittivity in soilsThere are several factors which affect the permittivity of a soil.

A soil consists of air, water, and solids. The permittivity of freewater is 80.36 at 20 °C (Roth et al. 1990); much larger than thepermittivity of most common soil minerals, which ranges between 3and 5 (Roth et al. 1990). This difference is due to the high ability ofthe water molecules to polarize compared to that of soil particles.

As there are significant differences between the permittivity ofa soil’s constituent components, it stands to reason that the per-mittivity of a soil is highly dependent on its water content (Ledieuet al. 1986). Therefore the most important effect on the permittiv-ity of a soil are its air:solids:water ratios. Hence the density of thesoil must be significant in determining the ARDP of a soil as thiswill directly affect the amount of air present. However, thisshould have a much smaller effect than the water content becausethe ARDP of soil minerals is much closer to the ARDP of air (ap-proximately unity) than that of water (Roth et al. 1990). The GWCcannot describe the volume of water surrounding a probe of finitelength. However, the VWC of a soil does take this into account.Therefore, to produce a relationship relating the ARDP to theGWC, some consideration must be given as to how to take thespecific volume of soil present at a particular GWC into account.This should be done without overcomplicating the proposed rela-tionship, which would reduce its applicability. One approach ad-opted is to use the soil’s dry density (Yu and Drnevich 2004).

There are however, additional complexities caused by boundwater and temperature effects (Craig 2004). Opinions vary withinthe literature as to the importance of such properties. For exam-ple, Roth et al. (1990) use temperature as the secondary input intothe ARDP to estimate the VWC of a soil, while Wang and Schmugge(1980) found that using sand and clay contents to estimate theamount of bound water produces a more accurate relationship.However, the amount and state of the bound water is not assimple as a relationship between the amount of clay and sandpresent. It has been found to be also dependent on the clay min-eralogy. For example, Smectite adsorbs significantly more waterthan Kaolinite (Craig 2004) due to its higher specific surface area,and therefore shows a higher amount of bound water (Thomaset al. 2010a). Therefore, as part of this research, existing relation-ships between ARDP and VWC were tested on different soils, andinvestigations were conducted to shed more light into the signif-icance of different parameters affecting ARDP, and ultimately,VWC.

Experimental methods

Soil samplesSoils from two separate sites located in Cambridgeshire, UK,

were used in this study, one comprising glacially derived clay(Diddington clay field, DCF), the other comprising sand and silt offluvial origin (Diddington pasture field, DPF). A number of soilswith slightly different properties were identified from both sitesand described in Table 1 according to BSI (1990). Disturbed sam-ples were taken in bags and undisturbed samples were takenusing monolith tins for geotechnical laboratory testing to charac-terize the soils, as per BSI (1990). The parameters measured forcharacterization purposes were field dry density (Mg/m3), particle

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density (Mg/m3), particle size distribution (%), Atterberg limits (i.e.liquid limit, LL (%) and plastic limit, PL (%)), and linear shrinkage,LS (%). The range of values measured for the soils studied fromboth sites are reported in Table 2. Although the soils at each sitevaried slightly (see Table 1), the two sites can be broadly classed as“clay” (DCF) and “sandy silts – silty sands” (DPF). Therefore, for themajority of the paper, the different horizons at each site were notdifferentiated.

Calibration of TDR and signal processingThe TDR used to obtain the ARDP and BEC was a Campbell

Scientific TDR100 in conjunction with CS645 probes. The probeshad three prongs: 75 mm long and approximately 7 mm apart(centre to centre). An air–water probe calibration to find the ap-parent permittivity was carried out on the TDR probes, as was theBEC calibration using liquids of varying conductivities similarto Curioni et al. (2012) as outlined by Heimovaara (1993) andHuisman et al. (2008).

Sampling for permittivity testingThe samples needed to comfortably house the 75 mm long TDR

probes to allow for accurate measurements and hence 100 mm by100 mm cylindrical sample pots were used. To avoid issues withelectrical interference affecting the readings, the sample potswere constructed out of plastic.

The soil samples were compacted into the cylinders in 5, 20 mmlayers and left for 24 h to allow pore water to equilibrate acrossthe sample. This is a similar approach to that recommended forBritish standard triaxial tests where it takes approximately 24 h toequalize sample pore pressure with cell pressure before testing(BSI 1990). Samples were sieved through a 5 mm sieve so therewere no obstructions to the TDR probe. Sieving was not antici-pated to compromise the results with respect to the field condi-tions as the probe prongs cannot fit around an obstacle largerthan 5 mm. Therefore particles of this size would not be involvedin any readings taken in the field. To keep soils as similar to thefield as possible, the measured field dry density was used as atarget for the compaction of the samples. The results are dis-cussed later in this paper.

This still produced a large range of dry densities with valuesranging between 1.3 and 1.9 Mg/m3. To check the effects of density,a laboratory sensitivity analysis was carried out, varying the drydensity for two soil types from the two sites by 10%.

Working with a large set of different soil types at a large rangeof water contents, one particular methodology could not be ap-plied to all samples (44 in total). Therefore two methodologieswere developed. These methods deal with the tendency for verydry clays to hold water unevenly in clusters.

Method 1 was used on fine-grained and coarse-grained sampleswith lower target water contents. It is based on the method ofstarting from a dry sample outlined in Quinones et al. (2003).

Initially the sieved soil was dried in an oven at 105 °C for aminimum of 24 h. This was necessary as the soil samples were to

be prepared at the densities found in the field from where the soilwas collected. All the fine-grained soils formed brick-like, sedi-mented chunks. These chunks were wetted to approximately10% GWC and were placed in a mixer that broke the damp, gravelsized chunks of soil into small granules without crushing the finegravel particles present. Breaking these by crushing the soil couldhave had a significant effect on the measured permittivity as itchanges the specific surface area of the soil, which in turn mayaffect the bound water content (Craig 2004).

The granules produced (see Fig. 1) were then dried in an oven fora second time. Since the volume of the cylinders was known andthe target dry density was known, using the assumption thatwater added was at the expense of air present in the soil, theamount of water to add to a sample was calculated.

The water was added to the sample using a plant mister toevenly distribute it through the soil. The small grains tended tohave visibly different water contents at this point (Fig. 1). There-fore the sample was wrapped tightly in cling film and allowed toequalize for 24 h before being packed into cylinders.

Method 2 was developed for fine-grained soil samples tested athigher water contents. As in method 1, the soil was wet sieved anddried to form brick-like chunks of soil. This soil of known dryweight was then saturated and thoroughly mixed. This took lon-ger if the soil was more plastic, and occasionally had to be leftovernight to allow the soil chunks to absorb the water. The re-quired mass of water for a target VWC was calculated based on thefield dry density, cylinder size, and the known dry weight of soilpresent. Therefore, the amount of water to be removed from thesample was calculated and the target mass of the sample derived.

To achieve the target mass, the sample was dried using an ovenat 105 °C for short intervals (no longer than 0.5 h) and then stirredvigorously so that no crusts of dry soil were allowed to form. Thiswas necessary due to the practicalities associated with the amountof soil that needed to be prepared (2.5 kg for each test). However,there was often desiccated soil around the edges of the container.Therefore, as with method 1, it was vital that the soil water shouldbe allowed to equalize before being packed into the cylinders. Theentire sample was carefully removed from the container and al-lowed to equalize for 24 h as per method 1.

To check that both methods were producing uniform samplesfor testing, each sample was subject to three water content testsby removing subsamples at different stages during sample prepa-ration and testing. One subsample was taken at the compactionstage and great care was taken to replace the removed volume ofsoil, and two when the sample was dismantled after testing; onefrom where the probe was inserted, and one using the rest of thesample. This meant that a representative VWC could be found forthe entirety of the sample in the cylinder.

The cylinder was sealed with silicone to stop evaporation, andfitted with a TDR probe that was secured and remained in placethroughout the duration of the testing (Fig. 2).

Table 1. Brief field descriptions of the soils found on the DCF and DPF sites according to BSI (1999).

Soil Brief descriptionField dry density(Mg/m3)

DCF SiteTopsoil Soft-firm brown slightly sandy slightly gravelly clay. 1.56Subsoil Stiff mottled light and dark brown thinly laminated slightly silty clay. 1.66Natural Stiff light brown slightly silty slightly gravelly clay containing chalk rockflour. 1.90Ditchfill 1 Stiff brown slightly gravelly silty clay. 1.61

DPF SiteTopsoil Loose grey slightly gravelly silty sand. 1.62Subsoil Dense brown slightly gravelly slightly clayey sandy silt. 1.66Ditchfill 1, 2, and 3 Loose brown slightly gravelly clayey sandy silt. 1.60; 1.31; 1.66Natural Uncompact sandy silt containing medium-spaced sand lenses 1.60

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To examine the effects of temperature, each sample was placedin an incubator at 0, 10, and 20 °C for 24 h. Three permittivity andBEC readings were taken at each temperature, and the mean ateach temperature was used for analysis. The GWC was deter-mined after the TDR measurement for all samples.

Results

VWC resultsThe results in Fig. 3 show a clear difference between the silty–

sandy soils and clay soils. Therefore two different empirical or soilspecific relationships between the VWC and ARDP were derived(eqs. (1) and (2) in Table 3). For comparison purposes, the Topp

et al. (1980) relationship is also shown in Fig. 3. It can be seen thatthe Topp et al. (1980) model works reasonably well for clay soils,but underpredicts the VWC at larger ARDP, while it underpredictsthe VWC for coarse-grained soils at ARDP values less than 15.Dirksen and Dasberg (1993) found that deviations from the Toppet al. (1980) equation were mainly due to variations in soil drydensity. Density sensitivity testing was carried out to see if thiswas true for the soils studied. The dry density of two representa-tive samples (one for each site) was varied by ±10% to observe theassociated variation in ARDP. These variations were found to benegligible. Additionally it was found that changes in temperatureproduced no noticeable effect on the measured ARDP as can beseen in Fig. 4, which shows the measured VWC versus the mea-sured ARDP for both soils and the two extreme temperatures of0 °C and 20 °C. The scatter indicates that there was no systematiceffect of the change in temperature and that the overall effectswere small. However, as expected (Campbell et al. 1949), temper-ature had a large impact on the measured BEC (not shown in thispaper).

Gravimetric resultsThe results obtained can also be expressed in terms of GWC.

GWC is obtained by dividing the VWC by the soil dry density(eq. (7)), assuming a density of water, �w, of unity (Yu and Drnevich2004)

(7) GWC �VWC�w

�d

where �d is the dry density (Mg/m3). It can be seen from Fig. 5 andTable 3 that there was a loss in accuracy as a result of using themeasured GWC rather than VWC (eqs. (3) and (4) in Table 3 showsmaller R2 values compared to eqs. (1) and (2)). This was expectedas the GWC does not account for the volume of water the TDRprobe is measuring. Therefore a more appropriate relationship isbetween GWC and ARDP normalized with dry density. Figure 6shows the improved relationships (eqs. (5) and (6) in Table 3) ob-tained after normalizing ARDP with dry density in line with theapproach taken by Thomas et al. (2010a, 2010b). However, from thedensity sensitivity results, dry density did not appear to signifi-cantly account for any additional variation of ARDP. Quinoneset al. (2003) found that the density of a soil only affected themeasured ARDP at extreme densities and the densities found hereare within the commonly encountered range in natural soils(Craig 2004).

Discussion

Testing reliabilityThe methods used produced measureable errors in both the

readings taken by the TDR and the measured water contents. TheGWC was taken on 3 specimens from each sample and the mea-sured variability was on average 0.33% GWC, with a maximumvariability of 0.90% GWC, while the TDR measurement was alsorepeated 3 times with the probe in the same position, whichresulted in a mean measurable error of 0.10, with a maximum

Table 2. Range of values for the soil geotechnical parameters of the soils studied.

Gravel (%) Sand (%) Silt (%) Clay (%)Particle density(Mg/m3)

Dry density(Mg/m3) PL (%) LL (%) LS (%)

DCFMin 6.3 16.3 45.6 21.9 2.58 1.46 18.0 40.0 10.5Max 8.6 22.0 52.6 30.9 2.83 1.90 22.0 48.0 15.2

DPFMin 8.1 32.9 13.3 6.0 2.60 1.30 15.0 24.0 6.5Max 33.3 47.4 43.0 14.0 2.69 1.86 17.0 30.0 8.4

Fig. 1. Visible variation in soil granules during sample preparation.

Fig. 2. Completed sample with TDR probe inserted.

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error of 0.50. Clearly, the variations were small and demonstratethe robustness of the experimental methodology.

Comparison with other relationshipsData from the laboratory testing have been plotted and com-

pared to a number of different empirical and semi-empirical mod-els developed on a large number of soils from the literature inFig. 7. The equations used are shown in Table 4. The Roth et al.(1990) model requires additional inputs of temperature and poros-ity to calculate water content. In Fig. 7, the Roth et al. (1990) modelis plotted for all three temperatures used in this research, with anassumed dry density value of 1.7 Mg/m3. The dry density was usedto calculate a value of porosity to input in the model (equal to1 minus the ratio of dry density divided by particle density).

The variation between different models is not large at low ARDPvalues with relationships varying by c. 5% VWC, although maxi-mum variance at higher ARDP values, especially between theWensink (1993) model and the other models, is approximately10%–12% VWC. More significantly, however, it can be shown thatnone of the models provide a good fit to the collected data acrossthe whole ARDP range for both soil types. In the DCF samples, allof the models overestimate and underestimate the water contentat high and low ARDP values, respectively, with the exception ofthe reasonable fit of the Wensink (1993) model. The reason for thisdeviation is that Wensink (1993) related the VWC with the ARDPmeasured at 1 GHz, which is less affected by dispersion and con-ductive losses, and in fact provides a better fit to the clayey soils.At low ARDP values, the opposite effect is true for the DPF samples

with the models underestimating the VWC in most of the mea-sured samples, although many of the models show a reasonable fitas the ARDP increases. These data fits highlight the need to choosea suitable model for the soil type, or if maximum accuracy isrequired, then a soil- and system-specific model should be devel-oped.

It is interesting to note that the Roth et al. (1990) relationshippredicts a wide variation of VWC for the three temperatures andsoils investigated in this research, which is in contrast to themeasurements shown in Fig. 4. Although temperature is knownto have a negative dependence on ARDP (Kaatze 1989), this effectis competing with the release of bound water (Wraith and Or 1999;Skierucha 2009) and increases in bulk electrical conductivity thatcan contribute to an increase in ARDP. Examination of the datashowed the net temperature effect on measured ARDP to be smalland it is thought that this is a result of the balance between thesecompeting effects, which largely cancel each other out. At highARDP values on DCF and low ARDP values on DPF, these temper-ature deviations are less apparent due to inaccuracies in the ARDP–VWC relationship, which provide more significant errors as shownin Fig. 7.

Factors affecting soil permittivityIt is clear from the previous discussions that several parameters

influence the measured ARDP, and it has been difficult to identifythe various relationships. To assess which soil properties affectedthe measured ARDP, a principal component analysis (PCA) wascarried out, which, to the knowledge of the authors, is not

Fig. 3. Relationship between VWC of a soil and its measured ARDP (by TDR) shown for clay soils (DCF) and sandy silts – silty sands (DPF). Toppet al. (1980) relationship is also shown for comparison. R2, square of the multiple correlation coefficient.

Table 3. Summary of equations derived from TDR measurements relating ARDP to VWC or GWC for different soil types.

Inputs Outputs (%) Soil type Equation R2 Equation No.

ARDP VWC Silty sands – sandy silts VWC � 0.0019�r3 � 0.1169�r

2 � 3.3208�r � 1.4288 0.96 (1)

Clays VWC � 0.0005�r3 � 0.0369�r

2 � 2.4478�r � 3.8036 0.97 (2)

GWC Silty sands – sandy silts GWC � 0.0007�r3 � 0.0913�r

2 � 2.2737�r � 0.8709 0.89 (3)

Clays GWC � 0.0007�r3 � 0.0354�r

2 � 1.5752�r � 2.4462 0.94 (4)

ARDP and �d (Mg/m3) GWC Silty sands – sandy siltsGWC � 0.006

�r3

�d� 0.2304

�r2

�d� 3.7823

�r

�d� 2.0189

0.94 (5)

ClaysGWC � 0.0006

�r3

�d� 0.038

�r2

�d� 2.3316

�r

�d� 2.2181

0.97 (6)

Note: �r, measured apparent relative dielectric permittivity; �d, dry density (Mg/m3).

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common practice in geotechnical engineering. However, as the soilis a complex system characterized by a number of interrelatedparameters, a PCA can be a useful way of describing this system.The advantage of the PCA is that it considers several variables at atime and gives an immediate picture of their underlying relation-

ships (i.e., correlations). This means that each parameter inputtedinto a PCA will be correlated with each other and the degree ofcorrelation determined, which is then expressed in the principalcomponents. A PCA consists of a mathematical procedure thatrotates the original data, organized in an n × p matrix, where n are

Fig. 4. Relationships between VWC of a soil and its measured ARDP (by TDR) shown for clay soils (DCF) and sandy silts – silty sands (DPF) at 0and 20 °C.

Fig. 5. Relationship between measured ARDP and GWC between clays (DCF) and sandy silts – silty sands (DPF).

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the observations (i.e., measurements) and p the parameters, mul-tiple times in the direction of greatest variance (Jolliffe 2002). Thefirst rotation is along the direction of greatest variance in the data,the second rotation is along the direction of the second greatest

variance, and so forth. New orthogonal and uncorrelated vari-ables, called principal components (PCs), are generated by thisprocedure and are a linear combination of the original parame-ters. Further details on the theory of PCA can be found in reference

Fig. 6. Relationship between measured ARDP divided by soil dry density and GWC.

Fig. 7. Variabiliy of VWC predictions obtained with selected empirical and semi-empirical relationships found in the literature. DCF and DPFmeasurements are shown for comparison.

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manuals such as Jolliffe (2002). The input parameters used in thecurrent analysis were: VWC, ARDP, BEC, temperature, particledensity, dry density, LL, PL, LS, and clay, silt, and sand contents.Temperature, dry density, VWC, ARDP, and BEC were different foreach measurement, whereas the other geotechnical parametersvaried for each soil type. The variables were normalized prior tothe PCA to make them comparable irrespective of their scale ac-cording to eq. (8):

(8) x ′ �x � �

�

where x= is the normalized variable used in the PCA, x is theoriginal variable, and � and � are the mean and standard devia-tion of the original variable, respectively. The function prcompimplemented in the stats package in the software environment Rwas used to perform the analysis. Table 5 shows the contributionof the original variables in the first four principal components,which are ranked according to the percentage of total variancethat they explain (i.e., PC1 accounts for most of the relationshipsbetween parameters, PC2 accounts for the second most importantvariance and so on). Figure 8 shows the percentage variance foreach PC and indicates that approximately 88% of variation wasaccounted for in the first four principal components. However,most of the variation was described by the first two principalcomponents (66% of the total variance), and therefore these havebeen selected for further analysis. The important relationshipsbetween variables would be described by these two principal com-ponents due to their high contribution to the total variance. Thetypical output of a PCA, called a “biplot”, displays the contribu-tion of the original variables and the observations in two selectedprincipal components thatrepresent the axes of the biplot. Vari-ables placed close to each other are positively correlated, variablesplaced at 180 ° to each other are negatively correlated and orthog-onal variables are not correlated. The size and direction of thevector indicates the contribution of the original variables in theprincipal components (see Table 5). Figure 9 shows the biplot ofPCs 1 and 2 for the properties of all the soils tested. As expected,the ARDP appears close to VWC, indicating that the two parame-ters were strongly correlated. The ARDP was also correlated withBEC, confirming that BEC was predominantly caused by solubleions in the pore water and therefore increased with water con-tent. This is in accordance with previous literature (e.g., Hartsocket al. 2000). Figure 9 also shows that the soil density had an impacton the measurement of ARDP. This is a significant result reported

by other authors (Jacobsen and Schjonning 1993; Malicki et al.1996) and confirms the importance of the soil solids in determin-ing the dielectric properties of the soil. Interestingly, ARDP wasslightly affected by clay content, but was not significantly influ-enced by any of the other geotechnical parameters measured,which are all approximately positioned orthogonally with respectto ARDP. Thomas et al. (2010a) found that ARDP measurements at1 GHz were related to LL for a range of fine-grained soils. However,the frequency used in this study to obtain ARDP was below500 MHz, therefore a direct comparison cannot be made. In addi-tion, the soils tested by Thomas et al. (2010a) showed predomi-nantly higher LL values, from 25% to 312%, compared to thelimited range investigated here (24%-48%, see Table 2). Figure 9also shows a small vector for temperature, orthogonal to ARDP,indicating that temperature was not an important parameter af-fecting ARDP. As mentioned above, previous authors reportedconflicting relationships between ARDP and temperature, a posi-tive one for clays due to the release of bound water, and a negativeone for sands that follows a similar behaviour to free water (Orand Wraith 1999; Skierucha 2009). However, for the soils studiedhere, these relationships were not evident, confirming, as alreadymentioned above, that these competing effects cancelled eachother out. A PCA was also run using the data from the two sitesseparately (not shown) and in both cases ARDP did not show cor-relations with temperature, nor did it show any different resultsfrom the ones described above. It must be pointed out that a PCA

Table 4. Summary of equations used for comparing relationships between VWC (%) and ARDP (�r).

Relationship Equation(s)

Curtis (2001) VWC � 0.000237�r3 � 0.03421�r

2 � 2.435�r � 2.86

Ledieu et al. (1986) VWC � (0.113��r � 0.1756)100

Roth et al. (1990) �w(T) � 78.54[1 � 4.579 × 10�3(T � 25) � 1.19 × 10�5(T � 25)2 � 2.8 × 10�8(T � 25)3]

c ��r

�ww �

�w

�w(20)a �

�a

�w(20)s �

�s

�w(20) � 0.45

VWC �

c

� (1 � �)s

� �a

w � a

100

Topp et al. (1980) VWC � ��5.3 × 10�2 � 2.92 × 10�2�r � 5.5 × 10�4�r2 � 4.3 × 10�6�r

3�Wensink (1993) �r�1GHz�

� 3.2 � 41.4VWC � 16.0VWC2

VWC � ��41.4 � �41.42 � 64�3.2 � �r�32

�100

Note: T, temperature (°C); , empirical soil parameter; �a, RDP of air; �r, ARDP; �r�1GHz�, ARDP at 1 GHz; �s, RDP of soil minerals; �w, RDP

of free water; a, c, s, w, ratios of RDP as defined in this table; �, porosity.

Table 5. Contribution of the original variables used in the PCA in thefirst four principal components.

Original variables PC1 PC2 PC3 PC4

ARDP 0.235 −0.327 0.384 0.035BEC 0.295 −0.213 0.282 0.015VWC 0.202 −0.326 0.446 0.005Temperature 0.050 0.026 0.099 0.661Gravel −0.321 −0.145 0.054 −0.262Sand −0.353 −0.079 0.201 −0.158Silt 0.305 0.225 0.006 0.332Clay 0.355 −0.037 −0.296 0.038Particle density 0.064 −0.325 −0.493 0.235Bulk density 0.168 −0.512 −0.023 −0.124Dry density 0.047 −0.403 −0.422 −0.174PL 0.307 0.258 0.051 −0.329LL 0.356 0.147 −0.093 −0.251LS 0.334 0.206 −0.011 −0.289

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analysis on each single site would not be very informative due tothe limited number of soils studied, which showed limited varia-tion of several of the geotechnical properties for each site(Table 2). In order for the PCA to be effective, it should be carried

out on a relatively large number of measurements and soil prop-erties covering a wide range of values. Interpretation of the PCAresults is important to avoid the association of parameters that infact are not correlated, but appear correlated for a fortuitous case.

Fig. 8. Percentage variance explained by each principal component.

Fig. 9. Biplot of principal components 1 and 2 for properties of all of the soils tested from both sites.

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This can happen if the range of values of the properties consideredis not large enough or if only a small number of measurementshave been made. The user must interpret the PCA results andmake judgements based on existing theory. Alternatively, the PCAmust be carried out on a large number of measurements over awide range of values. When this condition is met, the PCA isa powerful tool that can describe the soil characteristics with asingle plot.

From the biplot it is also possible to identify clusters of theexperimental observations and determine which variables af-fected them more significantly (observations and variables placedclose to each other). Three main clusters can be identified in Fig. 9.The two clusters on the left side portion of the plot correspond toDPF as clearly shown by the variables “sand” and “gravel” placedclose to them. On the right side, centred around the variable“clay”, the cluster corresponding to DCF is visible.

The fact that two clusters form in Fig. 9 can also be explainedby the fact that the DPF soils were tested at lower water contentsthan the DCF soils because of their lower LL; at this water contenta soil can no longer be compacted. It was found that for the DPFsite, BEC rose approximately linearly with water content. In theclays, however, it appeared to increase up to a certain VWC andthen reach a constant level (Fig. 10). Soils appear to reach a watercontent threshold above which the BEC is unaffected by VWC, andthis threshold has been found to vary for different soil types(Fig. 10). The sands and silts tested in this study are not expected toreach this water content threshold in normal field conditions.Hence, the fact that the two soils were tested over different rangesof water content can affect the biplot.

Estimation of GWC using TDRHaving discussed the different soil characteristics affecting ARDP

and hence VWC, methods are proposed to determine GWC usingTDRs as a more useful parameter for a geotechnical engineer on site.GWC is an easier parameter to derive from a site sample than a VWC,as a disturbed sample and the inexpensive and simple oven dryingmethod (BSI 1990) can be used. Hence GWC has become the mostcommonly used moisture content measurement across the geotech-nical industry, and is the basis of many correlations and calculationsused by geotechnical engineers on a day to day basis. Small changesin GWC can create large changes in undrained shear strength, par-

ticularly in low plasticity clays (Clayton 1979). Therefore, the abilityto either determine the instantaneous measurement of GWC with-out the need of any laboratory testing or to continuously monitorand measure GWC inexpensively with little laboratory testing wouldhave, for example, for the continuous monitoring of consolidationadjacent to a structure; the effects of seasonal weather and climatechange on ageing earthwork assets, the shrink–swell potential adja-cent to trees, and trafficability and moisture variation of clay soils onhaul roads.

As mentioned earlier, the TDR measured ARDP can be related toVWC or alternatively to GWC if normalized by dry density. Hence,TDR has the potential for being a very useful tool to geotechnicalengineers, provided that a measurement or estimation of thesoil’s dry density is available. Dry density is a fundamental soilproperty and relates directly to void ratio, making it very closelycorrelated to the strength and compressibility of a soil. Like GWC,it is the basis for many calculations used in geotechnical design,but unlike GWC, dry density requires more sophisticated labora-tory testing to be determined directly. For example, the volumedisplacement method (BSI 1990) has been used on the soils in thisstudy. For construction projects the amount of laboratory testingcarried out is often constrained by budget and time. This paperproposes three methods of relating GWC to measured ARDP val-ues based on the description of the soil, with different levels ofknown geotechnical properties needed. The selection of the mostappropriate method depends on time, budget, and available data.The different methods are described below, followed by furtherdetails on each method, including examples.

Method A — An in-depth site investigation and undisturbed sam-ples to carry out full laboratory testing including dry density mea-surement.

Method B — A basic or preliminary site investigation to obtainfield soil descriptions and disturbed samples for index and classi-fication tests.

Method C — A site walkover or desk study using published datasuch as those provided by the British Geological Society in the UKto obtain field soil descriptions.

All three methods rely on a measurement or estimate of the drydensity, which in turn can be used to convert VWC to GWC using

Fig. 10. Relationship between volumetric water content and bulk electrical conductivity for DCF and DPF sites measured by TDR at 10 °C.RMSE, root mean square error; Rsq (R2), square of the multiple correlation coefficient.

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eq. (7). In all the methods, the VWC is obtained by applying em-pirical, semi-empirical, or soil-specific models to the ARDP valuesmeasured using TDR. For the purpose of this paper, only the Toppet al. (1980) relationship is used to obtain the VWC as this is awell-established and commonly applied relationship. The differ-ence in the methods is thus purely based on the different ways ofobtaining the dry density values. Where necessary, the methodused to obtain the dry density values is explained in detail withexamples provided. The results obtained from applying the differ-ent methods on the soils presented in this paper are comparedand discussed.

Method AThis method requires the most laboratory work and is the least

dependent on engineering judgement. The measured dry densityfrom laboratory testing is used in eq. (7) to determine the GWVfrom the VWC. The results are presented in Fig. 11 showing themeasured and estimated GWC using this method. Since thismethod uses only measured laboratory data and the Topp et al.(1980) relationship, all deviations of the predicted value from theactual value of GWC arise from experimental errors and errors infitting Topp et al. (1980). It should be noted that only one densitymeasurement was taken for each sample and the GWC was mea-sured three times as discussed earlier.

Method BThis method uses the LL and LS from index testing and an

estimated saturated bulk density to determine the dry density.The estimated saturated bulk density, �b,sat (Mg/m3), of a soil canbe based on the standard soil description (BSI 1999) and publishedtypical values of saturated unit weights in BSI (1994) and areshown for some soils in Table 6. Table 7 shows the saturated bulkdensity estimated for the soils in this paper based on the soil

description given in Table 1. Now assuming that the LL (obtainedfrom index testing) is approximately equal to the saturation mois-ture content, the dry density can be calculated using eq. (9) as allthe voids are water-filled.

(9) �d ��b,sat

1 � LL

The results from this calculation are shown in Table 7. For highplasticity clay soils which shrink appreciably when dried, this willunderestimate the dry density of soils at low in situ water content,as the specific volume of clay particles increases significantly be-tween a dry state and saturation (Chertkov 2000). For soils whichare expected to be at low water contents or for high plasticityclays, it is therefore recommended that this effect is accounted forby applying information on the linear shrinkage obtained fromlaboratory tests (BSI 1990). As the linear shrinkage represents areduction in volume of a soil when it is dried from its LL to desic-cation as a percentage it will produce an increase in dry densityproportional to its volumetric shrinkage. To take account of thisfor clay soils, it is proposed to increase the dry density derived byeq. (9) by a percentage equal to the linear shrinkage.

Soils tested here have only been tested at moisture contentsaround the optimum moisture content for compaction to avoidproblems of compaction at higher moisture contents. This meansthat these soils are close to their shrinkage limit, meaning themajority of volumetric contraction compared to saturated soilwill have occurred (Chertkov 2000). However, for soils with in situwater content close to saturation, or which do not exhibit signif-icant volumetric shrinkage with drying, this use of linear shrink-age is not required. Figure 12 shows the measured versus calculated

Fig. 11. Estimated versus measured GWC for method A with underlying VWC based on Topp et al. (1980).

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GWC using this method and Table 7 contains the relevant param-eters.

If the LL is not known for eq. (9), the LL can be estimated frompublished geological literature and an accurate description of thesoil (e.g., CIRIA 1999) or the Casagrande plasticity chart (Craig2004) if the activity of the clay or silt is known, but clearly, thisinduces another level of uncertainty.

Method CThis method can be used when only the soil description from a

site walkover or published geological data are available. Neglect-ing the mass of air, the bulk density of a soil is defined by eq. (10):

(10) �b,m �ms � mw

V� �d � VWC�w

where �b,m is the moist bulk density (Mg/m3); ms and mw are themass of solid particles and water (Mg), respectively; V is the vol-ume of the sample (m3); �d is the dry density (Mg/m3); and �w is thedensity of water (Mg/m3), taken as 1. From a soil description areasonable bulk density value can be estimated using Table 6. Itshould be noted though that this estimation does not take ac-count of the change in bulk density with water content. The pro-posed values for the soils presented in this paper are provided inTable 7, including their ranges where appropriate. The dry densityvaries with water content (see eq. (10)) and hence is not constant

for the individual soils, therefore no values are provided inTable 7. Where there was a range of values, as shown in Table 6,the average bulk density value has been taken as the most appro-priate estimation, but a sensitivity study has been carried out andis discussed further in the next section as well as with error barsshown in Figs. 13a and 13b.

It should be emphasized that this approach relies on having adetailed soil description to reduce inaccuracy, but does make itsuitable in situations where only a desk study has been carriedout. Figures 13a and 13b show the results for the measured GWCand estimated GWC using this method for DCF and DPF, respec-tively, with the error bars indicating the possible range dependingon which value of bulk density was chosen.

Method comparisonThree different methods have been proposed to obtain GWC

(from VWC derived by relating it to the measured ARDP valuesusing TDR), based on knowing or estimating the dry density.Figures 11 to 13 show the estimated versus the measured GWC forthe three methods, respectively. All the methods show reasonableagreement between the measured and calculated GWC, althoughit can be seen that all the methods performed less well for the DPFsoils. It should be noted that errors can be induced by a number ofsources, including experimental errors when measuring ARDPand GWC, the errors of using Topp et al. (1980) in contrast to

Table 6. Typical bulk density and saturated bulk density values for a range of soils (after BSI 1994).

Bulk density, �b (Mg/m3)Saturated bulk density,�b,sat (Mg/m3)

Granular soil Loose Dense Loose Dense

Gravel 1.60–2.00 1.80–2.10 2.00 2.10Well graded sand and gravel 1.90–2.15 2.10–2.30 2.15 2.30Coarse or medium sand 1.65–2.00 1.85–2.15 2.00 2.15Well graded sand 1.80–2.05 2.10–2.25 2.05 2.25Fine or silty sand 1.70–2.00 1.90–2.15 2.00 2.15

Cohesive soil Bulk density, �b (Mg/m3)Saturated bulk density,�b,sat (Mg/m3)

Peat (very variable) 1.20 1.20Organic clay 1.50 1.50Soft clay 1.70 1.70Firm clay 1.80 1.80Stiff clay 1.90 1.90Hard clay 2.00 2.00Stiff or hard glacial clay 2.10 2.10

Table 7. Input parameters and derived dry densities for the three different methods proposed (values in brackets indicate the minimum andmaximum values for the density based on measurements or Table 6).

Method B

Soil

Method A: Averagemeasured drydensity (Mg/m3)

Measuredliquidlimit (%)

Est. satdensity(Mg/m3)*

Est. drydensity(Mg/m3)†

Measured linearshrinkage (%)

Est. drydensity(Mg/m3)

Method C: Est. bulkdensity (Mg/m3)*

DCF topsoil 1.54 (1.46–1.59) 48.00 1.90 1.39 15.2 1.51 1.75 (1.7–1.8)DCF subsoil 1.65 (1.65–1.65) 47.00 1.9 1.50 13.7 1.70 1.90DCF ditchfill 1 1.59 (1.57–1.61) 41.00 1.9 1.52 10.8 1.60 1.90DCF natural 1 1.83 (1.58–1.9) 40.00 1.9 1.53 10.5 1.69 1.90DPF topsoil 1.62 (1.60–1.64) 30.00 2.00 1.57 — 1.57 1.85 (1.7–2.0)DPF dubsoil 1.65 (1.61–1.67) 25.00 2.15 1.75 — 1.75 1.90DPF ditchfill 1 1.56 (1.54–1.57) 27.00 2.00 1.61 — 1.53 1.85 (1.7–2.0)DPF ditchfill 2 1.36 (1.30–1.64) 27.00 2.00 1.61 — 1.53 1.85 (1.7–2.0)DPF ditchfill 3 1.65 (1.65–1.66) 24.00 2.00 1.64 — 1.56 1.85 (1.7–2.0)DPF natural 1.83 (1.79–1.86) 26.00 2.00 1.62 — 1.62 1.85 (1.7–2.0)

*From Table 6.†Using eq. (9).

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soil-specific calibrations, and errors when obtaining the dry den-sity either through measurements or the alternative methods pro-posed. The results presented in Fig. 11 are only based on laboratorymeasurements as well as the application of Topp et al. (1980). Theerrors of using Topp et al. (1980) to determine the VWC for thesoils presented in this paper is also apparent in Fig. 3, and hasbeen discussed previously. As Topp et al. (1980) performed lesswell for the sandy silts – silty sands (DPF), it is not surprising thatthe calculated GWC values for DPF (see Fig. 11) deviate furtherfrom the measured GWC in contrast to the DCF values. Overallthough, 98% and 92% of the values for DCF and DPF, respectively,are within a ±5% GWC envelope, and the mean errors are 1.69%GWC and 2.00% GWC, respectively (see Table 8).

Methods B and C rely on the estimation of the saturated bulkdensity and bulk density respectively to determine the dry den-sity. The error analysis for methods B and C (see Table 8) show thatthe percentage of data within the ±5% GWC envelope is less thanmethod A. This is not surprising, as the dry density is based onestimation requiring engineering judgement. It can also be seenthat the error increases more for DPF compared to DCF. A possibleexplanation is the wider possible range of bulk density values (seeTable 6) for silts and sands compared to clays. This is also visiblein Fig. 13b, which shows larger error bars for DPF compared toFig. 13a for DCF.

However, it should be pointed out that all three methods per-formed well in determining the GWC. Not surprisingly, method A,based on only measurements, provided the best fit. The strengthof methods B and C is the fact that no, or only very simple, labo-ratory tests are needed. Based on the accuracy required for aspecific project, as well as the available soil information, thegeotechnical engineer should choose the most appropriate method.It is also important to note that the accuracy can be increased by

using a soil-specific calibration to determine the VWC from ARDPmeasurements and the data lying within the ±5% GWC envelopeincrease to between 96% (method C) and 99% (method A). If this isobtained, the engineer will most likely have carried out extensivelaboratory tests to characterize the soil, and thus should be in aposition to use method A.

Furthermore, for projects that require high accuracy in the de-termination of GWC, soil specific empirical calibrations may berequired, and more rigorous methods such as the one presentedby Jung et al. (2013) should be preferred. However, this methodrequires the use of bespoke TDR probes together with dedicatedlaboratory testing specific to the soil under investigation.

ConclusionsTo create a uniform soil sample from a fine-grained soil, consol-

idation methods can take weeks. This paper described a poten-tially less time consuming method using a combination of ovendrying and equalization time that proved to be very successful forthe TDR experiments conducted in this research, and produced amean error of less than 0.33% GWC across a sample.

In the published literature, variations in predicted VWC is notlarge at low ARDP values (c. 5% VWC), but can increase to approx-imately 10–12%VWC at higher ARDP values. The data fits with themeasurements showed that all models either overestimated orunderestimated the VWC for the soils presented in the paper andthat soil-specific relationships between ARDP and VWC need to bedeveloped to increase the accuracy. In measuring the ARDP of asoil, sands and clays are expected to behave in a very differentmanner. This was corroborated by the derivation of two separaterelationships between VWC and ARDP for the soil samples fromtwo sites, DPF and DCF. Therefore, a relationship which has been

Fig. 12. Estimated versus measured GWC for method B with underlying VWC based on Topp et al. (1980).

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designed to apply to any soil type will be an approximation be-tween a clay dominant and a sand dominant soil.

No measureable effect on ARDP due to temperature was found.This was confirmed by a PCA, although soil conductivity (BEC) isaffected by temperature. This was in contrast to findings by otherresearchers, for example Roth et al. (1990). It was hypothesizedthat this is due to the conflicting effects of the release of boundwater and the temperature dependent permittivity of water thatis more important in saturated soils.

Dry density does not appear to directly affect the measuredARDP for the density range analyzed during the sensitivity analy-sis, but it showed some effects in the PCA analysis on all soils as

the actual dry density of the soils varied by more than the 10% usedin the sensitivity analysis. The dry density can be used to add thevolumetric dimension to the relationship between GWC andARDP, improving its accuracy from an R2 coefficient of 0.88 to 0.94for the silty sands and sandy silts, and from 0.94 to 0.97 in theclays used in this study.

Although the results from the PCA mainly confirmed the influ-ence of different soil parameters, the potential of this method wasdemonstrated and it is believed that this analysis would be evenmore useful for soils with a larger range of particle size distribu-tions and Atterberg limits. The advantage of a PCA is that it con-

Fig. 13. Estimated versus measured GWC for method C with underlying VWC based on Topp et al. (1980) for (a) DCF and (b) DPF.

0.00

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35.00

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WC

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Linear (01:01) Linear (+/- 5%)

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(b)

Table 8. Comparison of errors in the determination of GWC for selected models using the different estimationmethods.

Method A Method B Method C

DCF DPF DCF DPF DCF DPF

Absolute mean error (GWC %) 1.69 2.00 2.38 2.26 1.93 2.80Max error (GWC %) 8.12 12.09 6.45 11.58 6.05 12.02Standard deviation error (GWC %) 1.37 1.80 1.58 2.17 1.50 2.16Data within ±5 % GWC envelope (%) 98 92 94 84 96 84

Note: Total sample set size was 174 and 184 for DCF and DPF, respectively.

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siders several variables at a time, giving an immediate picture oftheir underlying relationships.

Three different methods have been proposed to determine theGWC from the VWC, derived using Topp et al. (1980), and mea-sured or estimated values for dry density. All three methods havea number of different error sources, but overall performed wellwith between 83% and 92% of data for DPF and between 95% and98% of data for DCF lying within the ±5% GWC envelope, and theabsolute mean errors ranging from 2.00%–2.76% for DPF and1.69%–2.02% for DCF. Therefore, the proposed methods have thepotential to extend the use of TDRs to those communities who areinterested in GWC and not VWC.

AcknowledgementsThe authors would like to thank the University of Birmingham,

and the “Detection of Archaeological Residuals using remote sensingTechniques” (DART) AH/H032673/1 and “Mapping the Underworld”(MTU) EP/F065965/1 projects for access to soil samples, testingequipment, and soil data.

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